spectral re-growth due to hpa nonlinearity

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Spectral broadening effects of high-power amplifiers in MIMO-OFDM relayingchannels

EURASIP Journal on Wireless Communications and Networking2013,

2013:32 doi:10.1186/1687-1499-2013-32

Ishtiaq Ahmad ([email protected])Ahmed Iyanda Sulyman ([email protected])

Abdulhameed Alsanie ([email protected])Awad Kh Alasmari ([email protected])

Saleh A Alshebeili ([email protected])

ISSN 1687-1499

Article type Research

Submission date 14 June 2012

Acceptance date 10 November 2012

Publication date 15 February 2013

EURASIP Journal on WirelessCommunications andNetworking
mailto:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]:[email protected]


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Spectral broadening effects of high-power amplifiers

in MIMOOFDM relaying channels

Ishtiaq Ahmad1

Email: [email protected]

Ahmed Iyanda Sulyman1*

*Corresponding author


Abdulhameed Alsanie1


Awad Kh Alasmari1


Saleh A Alshebeili1,2


1Department of Electrical Engineering, King Saud University, Riyadh, Saudi

Arabia

2KACST Technology Innovation Center RFTONICS, King Saud University,

Riyadh, Saudi Arabia

Abstract


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Keywords

Spectral re-growth, Amplifier nonlinearity, Spectral mask, MIMOOFDM, Relaying

channels

Introduction

Fourth-generation (4G) broadband communication systems need to provide ultra-high data

rate services in order to meet the requirements of future high-bandwidth multimediaapplications over cellular systems such as the digital TV distributions and interactive videos

planned in the WiMAX and LTE-advanced. Among the candidate physical layer technologies

that can be deployed to achieve these goals, MIMOOFDM is the most potent solution that

can provide such high data rate at high spectral efficiencies. Compared to the single-carrier

systems however, OFDM has a large peak-to-average-power ratio [1,2] which makes it very

sensitive to high-power amplifier (HPA) nonlinearities at the RF stage of the transmission

chain [3]. There are two important effects of the HPA nonlinearities introduced in the

transmitted OFDM signals: in-band and out-of-band distortions. The in-band distortiondegrades bit error rate (BER) performance and capacity of the cellular operator [4-10],

whereas the out-of-band distortion arising from the spectral broadening effect of the HPA

affects other users operating in the adjacent frequency bands [11-15]. While the BER and

capacity analysis of OFDM relay links in the presence of HPA nonlinearity are fairly well

understood [5 and references there in], the effects of HPA on out-of-band emissions for

OFDM relay link are not yet studied to the best of the authors knowledge. Out-of-band

emissions are strictly monitored by the cellular regulators using the concept of transmit

spectrum mask. Transmit spectrum mask is the power contained in a specified frequency

bandwidth at certain offsets, relative to the total carrier power. In the 4G system such as

WiMAX and LTE-advanced, strict limits have been specified for the spectrum masks. Figure

1 displays the spectrum mask of the IEEE 802 16 signal specified in the WiMAX standard


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the spectral re-growth. It is important to note that OFDM signals share some similarities with

CDMA signals in this regard. Recently also, Gregorio et al. [17] proposed a MIMO-

predistortion (MIMO-PD) system that tries to compensate crosstalk and IQ imbalance insingle-hop MIMOOFDM communication systems, where they have shown that some

reduction in the spectral re-growth can be achieved using the proposed MIMO-PD system.

The effectiveness of such a compensation scheme in a multihop environment is however not

yet known.

All the above-cited studies, and several others in the literature however, focused on the

spectral re-growth due to HPA nonlinearity in a single-hop communication system. Recently,the two prominent 4G cellular systems, WiMAX and LTE-advanced, have defined relaying

as an integral part of the network design [18,19]. Thus, MIMOOFDM signals transmitted in

the 4G systems will frequently pass through one or more relay hops from source node to the

destination node. Investigating the level of adherence to set limits on spectral broadening in

cellular systems employing relaying technologies is therefore a deployment imperative. To

the best of the authors knowledge, no work has presented a detailed study of the broadening

effects of HPA nonlinearity on the spectrum of MIMOOFDM signals in multihop relaying

channels.

In this article, we characterize for the first time in the literature, the cumulative spectral

broadening effects of multiple HPAs when MIMOOFDM signals are transmitted over

multihop relaying channels. Expressions for the PSD of a MIMOOFDM signal are

presented over multihop relay channels, each equipped with nonlinear HPAs. It is shown

that due to the cumulative effect of the multiple HPAs in a MIMO link, and the cascade

effect of many relaying channels in a multihop relay link, significant broadening effect occur

which is much more than what would be observed in a single-hop transmission such as those

characterized in [11-15]. We also show that for the amplify-and-forward (AF) and

demodulate-and-forward (DemF) relaying options, the resulting cumulative re-growth may

lead to spectral mask violations after a few relaying hops is traversed by the transmitted


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multihop MIMO relaying channels H1,,HR, associated with R fixed or mobile relaying

nodes, to the destination node as shown in Figure 2.

Figure 2HPA nonlinearity model for MIMOOFDM relaying channel.

The MIMO channel matrix for each ith hop transmission Hi, i= 0, 1,, R, is an nN nN

block diagonal matrix, with the kth block diagonal entriesH[K]icorresponding to the fading

on the kth OFDM subcarrier, k = 0, 1,, n 1, modeled as independent and identically

distributed (iid) random variables taken from zero mean complex Gaussian distribution, with

unit variance. We assume that the set of random matrices {H0,,HR} are independent, andthat AF, DemF, or DF relaying options could be employed at the relay nodes [5,20]. We also

assume that the BS and all the relay stations (RSs) employ similar nonlinear HPAs which

introduce similar nonlinear distortions per hop, in the transmitted signal. A consequence of

this assumption is that if the BS or any of the RS employ a nonlinear HPA with nonlinearity

level more or less than the other devices, then the contribution of that device to the overall

spectral broadening will be more or less than estimated in this analysis. We can express the

transmitted symbol in polar coordinate as

)()()( tjetrtx = (1)

where r(t) is the amplitude and (t) is the phase of the input signal into the HPA. The signal

at the output of the HPA can then be expressed as

)()]([)(

tjetrgtx

= (2)

where g[r(t)] is a complex nonlinear distortion function, which only depends on the envelope

of the transmitted symbols. The nonlinear distortion function can be expressed as


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where Ais the small-signal gain, andAisis the input saturation voltage of the HPA. Let x(t)

denote the input signal into the HPA, and we assume that x(t) is Gaussian distributed.

Therefore, according to the Bussgangs theorem, the output of the HPA when the input is aGaussian process is given as [22,23]

)()()( twtkxtx += (5)

where k (i.e., 0 k1) is an attenuation factor for the linear part which represents the in-

band distortion, and w(t) is a nonlinear additive noise which represents the out-of-band

distortion. w(t) is a zero-mean complex Gaussian random variable (r.v), with the in-phase andquadrature components mutually iid, and with variance w2. The in-band and out-of-band

distortion terms can be calculated as [24]

*

*

avg 0

{ ( ) ( )} 1 ( ) ( )

{ ( ) ( )}

E x t x tk rx r f r dr

E x t x t P

= =

(6)

* 2 2

2 * 2 22

avg 0

{| ( ) | } | | 1 | ( ) | ( ) | |{| | }

w E x r k x r f r dr kE x P

= =

(7)

where * denotes complex conjugation, Pavg=E[|x|2] is the average input energy per symbol,

andf(r) is the probability density function (PDF) of the envelope of the input signal into the

HPA (i.e., r= |x|). The PDF of r is Rayleigh distribution (sincex(t) is assumed Gaussian).

The closed-form expressions for the in-band and out-of-band distortion parameters for the

SEL HPA model are calculated by substitutingf(r) into Equations (6) and (7) to obtain

* 2 22 * 2 2

2

avg 0

{| ( ) | } | | 1| ( ) | ( ) | |

{| | }w

E x r kx r f r dr k

E x P

= =

(8)


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)()()( 00 ttt wxx += (11)

where the vector1 ( ) [ ( ), , ( )]Nt x t x t =x and )( tx

j

are the output of the HPA at the jthtransmitting antenna of the BS when the input to the amplifier isx

j(t). 0is anNNdiagonal

matrix, where k0jrepresents the scaling factor of the linear part (in-band distortion) at the jth

transmit antenna of the BS. w0(t) = [w01(t), , w0

N(t)], and w0

j(t) is the nonlinear distortions

noise (out-of-band distortion) due to HPA at thejth transmitting antenna of the BS. The PSD

of a signal is commonly estimated by computing the autocorrelation function of the signal

followed by a Fourier transform, using the well-known WienerKhintchin theorem [25]. The

PSD of the OFDM signal at the output of the nonlinear HPA at the jth transmit antenna of aMIMOOFDM transmitter is given by

defPfjj

xx

j

xx jjjj2

)()(

+

=

(12)

where )( fPj

xx jj and )( j

xx jj represent the PSD and autocorrelation function of the OFDMsignal at the output of the HPA at the jth transmitting antenna. The autocorrelation function

for the output of the HPA at thejth transmitting antenna can be computed as

)()(||

})]()[({})]()[({||

})]()()][()({[

})]()[({)]()[(2

1lim)(

00

20

002

0

0000

*

jjjj

jj

j

jjjjj

jjjjjj

T

T

jjjj

Txx

k

twtwEtxtxEk

twtxktwtxkE

txtxEdttxtxT

wwxx +=

+++=

++++=

+=+=

(13)


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+

= dffPj

ww

j

w jjj)(

000

2

(15)

Using the result from [26, Equation (16)], Equation (15) can be approximated as

BfPj

ww

j

wjjj )(000

2

, whereBdenotes the bandwidth of the signal. This approximation is valid if

the spectrum of w0j is flat across the bandwidth, which is true for the subcarrier-based

analysis considered here. As the variance of the nonlinear noise due to HPA increases, the

spectral re-growth of the transmitted OFDM signal increases as can be observed from

Equation (15). Since the analysis above gives estimate of the spectral re-growth due to HPA

per transmitting antenna, then for MIMOOFDM system with Ntransmitting antennas, the

overall spectral re-growth that occur due to HPA nonlinearity is given by

0 0 0 0

MIMO

1

( )j j

Nj

w w w wj

P P f=

=

c

.

PSD of the nonlinearly amplified OFDM signals at RSs

Next we calculate the PSD of the nonlinearly amplified OFDM signals at RSs. For this

analysis, we consider two cases. In the first case, we consider that each RS has ability to

perform MIMO signal processing on the received signal before amplifying and forwarding it

onto the next hop, and thus we could examine the spectrum of the OFDM symbols obtained

at each receiving antennas of the RS. This case corresponds to the DemF relaying option. In

the second case, we consider that the RS does not have ability to perform MIMO signal

processing on the received signal before forwarding onto the next hop. The RS simply AF the

received OFDM signals at the RF stage without demodulating the OFDM signal. This case

corresponds to the AF relaying option. AF has the best latency performance, and is attractive


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N 1 complex additive noise vector and Nij[l] represents the iid zero-mean complex AWGN

noise on the jth transmit antenna in the ith hop for the lth subcarrier.

1 1 1 1

1 2[ ] [ [ ] [ ] [ ]]N TR R R RY l Y l Y l Y l= is anN 1 received OFDM symbol vector in FD at the first RS

and 10

01

[ ] [ ] [ ] [ ]Nj j

R jm mmY l H l X l N l

== + is the received OFDM symbol at the jth received

antenna of the first RS for the lth subcarrier. We assume that the channel between the BS and

the RS is known at the RS. Thus, we can employ MIMO Zero-Forcing or MIMO minimum

mean square error technique for the MIMO signal processing at the RS for the DemF relaying

option as

1 1,DemF 0[ ] [ ] [ ]R RY l l Y l= G (17)

where

( )

( )

1

0 0 0

0 10 0 0 0

[ ] [ ] [ ] : ZF[ ]

: MMSE[ ] [ ] [ ] [ ]

H H

H H

l l ll

l l l l

= +

H H HG

H H Q I H

(18)

and Q0[l] = E[(H0[l]W0[l] + N0[l])(H0[l]W0[l] + N0[l])H

]. Here, we used the ZF technique for

simplicity. The received symbol at the input of the first RSs HPA can then be expressed as

[ ] [ ] [ ] [ ] [ ]

[ ] [ ] [ ]

1 ,DemF 0 0 ZF 0

0 0 0'

RY l K X l W l G l N l

K X l W l N l

= + +

= + +

(19)

where 1 1 1 11 2

,DemF ,DemF ,DemF ,DemF[ ] [ ] [ ] [ ]

TN

R R R RY l Y l Y l Y l = is an N 1 received OFDM symbol


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1,DemF 1 0 1 1 1 0 1 1 0 1 ( ) ( ) ( ) ( ) ( )j j j j j j j j j j j jR t k k x t k w t k n t w t = + + +y

(21)

where n0j(t) and w0

j(t) are, respectively, the thermal noise and the nonlinear noise of the

HPA, propagated from the first hop transmission. w1j(t) and k1

jare the HPA distortion terms

introduced by the first RS. To calculate the PSD of the output of the HPA at thejth transmit

antenna of the first RS, we calculate the autocorrelation function of the output of the HPA at

thejth transmit antenna of the RS as

1 1 1 1,DemF ,DemF

1 0 1 1 1 0 1 1 0 1

1 0 1 1 1 0 1 1 0 1

2 2 2 2

1 0 1 1

( ) { ( )[ ( )] }

[ ( ) ( ) ( ) ( )]

[ ( ) ( ) ( ) ( )]

( ) | | | | ( ) ( ) |j j

j j j H

R R R R

j j j j j j j j j j

j j j j j j j j j j H

j j j j

x x

E y t y t

k k x t k w t k n t w t E

k k x t k w t k n t w t

k k k

= +

+ + + =

+ + + + + + +

= + 0 00 0 1 1

2 2

1 12

1

( ) | | ( )| ( ) ( )

j j

j j j j

j j

n nj

w w w w

k

N

+ +

(22)

where

1 1

1

[ ] {[( ) ][( ) ] }

{[ ] }

1

H H H H H H

i i i i i i i i

H

i i

N

E E

E

IN

=

=

=

G G H H H H H H

H H

Thus, the PSD of the OFDM signal at the jth antenna of the RS is computed from the

autocorrelation function using WienerKhintchin theorem and is given as

2 2( ) | | ( )

j jk P f (23


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12 2( 1) 2 2( )

,DemF

01

2 2( )

0

( ) ( ) (| |) ( ) ( ) (| |) ( )

1( ) (| |) ( ) ( )

j j j jm m

j j j jp p R R

Rj j R j R j R R m

RR

mR

j R R p

p

P f k P f k P f

k P f P f N

+

=

=

= +

+ +

x x w w

n n w w

(25)

Case II: AF relaying system

In AF relaying system, the received symbol at the input of the HPA of the first RS (R1) in FD

is given by

1 0 0

0 0 0 0

[ ] [ ] [ ] [ ]

[ ] [ ] [ ] [ ] [ ]

RY l l X l N l

l X l l W l N l

= +

= + +0

H

K H H

(26)

where 1 1 1 11 2[ ] [ [ ] [ ] [ ]]N T

R R R RY l Y l Y l Y l=

is an N 1 received OFDM symbol vector, and

[ ]1jRY l is the received OFDM symbol at the jth received antenna of R1for the jth subcarrierand is given by

][][][][][

][][][][

01

0

,1

0

,0

0

1

0,

1

lNlWlHmXlHk

lNmXlHlY

j

N

m

m

mj

N

mmj

m

j

N

m

mmj

j

R

++=

+=

==

=

(27)

The received OFDM signal at the jth receive antenna of R1 is then amplified with an

amplification factor 1j

as shown in Figure 2b The amplification parameter


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1

1

,AF ,AF 1

1

( ) ( ) ( ) ( )m m

Nj j j m j j j j j

R m m jl R m m m m

l

y t k h y t k n t w t

=

= + +

(30)

Then the PSD of the transmitted OFDM symbol at the output of the HPA at the jth transmit

antenna for the case m= 1 is given as

1 1 0 0

1 10 0

2 2 2 2 2

,AF 1 1 0 1 1

1 1

2 2

1 1

( ) ( ) | | | | ( ) ( ) | | ( )

( ) | | ( ) ( )

l l l lR R

j j l l

N Nj j j l j j

x x w wl l

j j

w wn n

P f k k P f k P f

k P f P f

= =

= +

+ +

(31)

Similarly, the general expression for the PSD of the transmitted OFDM symbol at the output

of the HPA at thejth transmitting antenna of the Pth RS is derived for AF relaying system as

1 1 1 1

1 1

2 2 2 2 2

,AF 1

1 1

2 2

( ) ( ) | | | | ( ) ( ) | | ( )

( ) | | ( ) ( )

l l l lR RP P P P P P

j j l lP PP P

N Nj j j l j j

P P P P PR R w wl l

j j

P P w wn n

P f k k P f k P f

k P f P f

= =

= +

+ +

(32)

where)(

11

fP lP

lP RR is the PSD of the transmitted OFDM symbol at the output of the HPA at the

lth transmitting antenna of the (P 1)th RS.

Simulation results and discussions

In our simulation setup, we consider multihop MIMOOFDM system for n = 1024

subcarriers and different number of transmit and receive antennas. We adopt 1024-FFT

downlink sub carrier allocation scheme defined in the WiMAX standard [16] as shown in


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severe power penalty. A popular approach is to clip the high peaks in the OFDM signal to

enable linear amplifications [27]. However, clipping operation itself is a nonlinear process

and it results in in-band and out-of-band distortions. The SEL model employed in oursimulation captures this HPA model. Figure 5 depicts the output of the HPA when the OFDM

signal in Figure 4 is passed through HPA for different values of the CR. It is easy to observe

from this figure that as the CR increases, the severity of the nonlinearity decreases and the

time waveform of the output signal from the HPA approaches the input signal into the HPA.

However, large clipping ratio incurs severe power penalties; therefore, there is a trade-off

between HPA power efficiency and nonlinearities introduced.

Figure 44-QAM, 1024 OFDM signal at the input of the HPA before clipping.

Figure 54-QAM, 1024 OFDM signal at the output of the HPA after clipping with CR of

0 and 6 dB.

Figure 6 shows the effect of HPA nonlinearity on the spectrum of OFDM signal for different

CRs. For this simulation, we used the Welchs modified periodogram method for the

estimation of the PSDs with the following parameters: 50% overlap between the segmentsand Hamming window. Welch function take into account the abrupt changes of the phase

between the two successive symbols. It is observed from this figure that there is an in-band

amplitude attenuation and an out-of-band spectral re-growth observed in the spectrum of the

output signal from the HPA, compared to its input. This confirms our earlier observations

from the analysis. It is also observed from the figure that as we back-off the amplifier from

the saturation region by increasing the CR, the out-of-band distortion decreases; however, the

in-band amplitude attenuation increases resulting in more in-band signal power attenuation.

This results in significant power penalty, making the use of large CR as a means of avoiding

HPA nonlinearity unaffordable in practice in the cellular systems due to the need to transmit

certain power levels in order to meet signal quality requirements at cell edges. In [27], it is

shown that at CR = 1 4 dB the distortion introduced by the HPA when transmitting OFDM


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Figure 8 presents the spectrum of the nonlinearly amplified OFDM signal at RSs, for

different number of relay hops, using DemF relaying option and CR = 1.4 dB. It is observed

from these results that the out-of-band distortion (i.e., spectrum re-growth in adjacent band)increases as the OFDM signal is relayed across multiple RSs, as observed earlier from the

analytical results in Equation (25). Thus, the WiMAX spectral mask displayed in Figure 1

would easily be violated when large numbers of relay hops are involved. Figure 9 compares

the effect of HPA nonlinearity on the spectrum of the relayed OFDM signals using AF and

DemF relaying configurations. The spectrum of the relayed OFDM signals using DF relaying

option is also included in the figure for reference. As expected, it can be observed from this

figure that there is a higher spectral re-growth in AF relay option than in the DemF relay

option. Also comparison between the spectral re-growth in DF relay option with DemF and

AF relay options, for different values of SNR at the RS, shows that less severe spectral

broadening is observed for the DF relaying option than the other two. It should be noted that

these results were evaluated from the analytical expressions derived above, which hold for

any CR. Therefore, the relative performance of DF, DemF, and AF relay options depicted in

this figure hold also for other values of CR.

Figure 8Effect of HPA nonlinearity on the spectrum of OFDM signals for differentnumber of relay hops (DemF, CR = 1.4 dB, SNR = 15 dB).

Figure 9Effect of HPA nonlinearity on the spectrum of OFDM signals for AF, DemF,

and DF configurations at RSs (CR = 1.4 dB, SNR = 10 dB).

Next we present results for the case when we window the OFDM signal using linear-phase

finite-impulse-response (FIR) digital filter before passing it through the nonlinear HPA,

similar to the set up used for the works in [15,28-30]. Since the analysis did not model the

effect of filtering, this part of the study is conducted solely by simulations. We use band-pass

equi-ripple FIR filter with 110 coefficients and pass-band 0.2 0.6, where = 1

corresponds to the Nyquist frequency for our simulation Figure 10 shows the effect of HPA


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the general mobile multihop relaying (MMR) system where data could traverse any number

of relay hops from source to destination has widely been studied theoretically [20,31,32],

only the 2-hop version such as those proposed by the IEEE 802.16j group [18] may beadvised for any practical deployments in MIMOOFDM transmissions because of the

potentials for spectral mask violations when going beyond 2-hop transmissions as shown in

these results. In Figure 12, the effect of HPA nonlinearity on DF-relayed OFDM signal is

presented. It can be observed from this figure that less severe spectral broadening is observed

for the DF relaying option. However, due to the latency problems associated with the DF

relaying option which degrades quality of broadband signals, AF or DemF are the preferred

candidates for broadband transmissions over relaying channels and therefore the spectral

broadening issues observed here must be given considerable attentions in the design of

broadband multihop-relaying systems.

Figure 10Effect of HPA nonlinearity on the spectrum of filtered OFDM signals at theBS for different CRs.

Figure 11Effects of HPA nonlinearity on the spectrum of filtered OFDM signals in

multihop relay channel (CR = 1.4 dB, SNR = 10 dB at each RS), DemF relaying at RSs.

Figure 12Effects of HPA nonlinearity on the spectrum of filtered OFDM signals in

multihop relay channel (CR = 1.4 dB, SNR = 10 dB at each RS), DF relaying at RSs.

Conclusions

This article presents new insights on the out-of-band spectral re-growth due to HPAnonlinearities when MIMOOFDM signals are transmitted over multiple relay channels.

Expressions for the PSD of a MIMOOFDM signal are presented when it is transmitted from

a BS to the MS via multiple RSs, all equipped with nonlinear HPAs. It is shown that


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References

1. S-H Wang, C-P Li, A low-complexity PAPR reduction scheme for SFBC MIMO-OFDM

systems. IEEE Signal Process. Lett. 16(11), 941944 (2009)

2. Y Wang, W Chen, C Tellembura, A PARP reduction method based on artificial bee colony

algorithm for OFDM signals. IEEE Trans. Wirel. Commun. 9(10) (2010)

3. E Costa, S Pupolin, M-QAM-OFDM system performance in the presence of a nonlinear

amplifier and phase noise. IEEE Trans. Commun. 50(3), 462472 (2002)

4. AI Sulyman, M Ibnkahla, Performance analysis of nonlinearly amplified M-QAM signals

in MIMO channels. Eur. Trans. Telecommun. 19(1), 1522 (2008)

5. T Riihonen, S Werner, F Gregorio, R Wichman, J Hamalainen, BEP analysis of OFDM

relay links with nonlinear power amplifiers, in Proceedings of the 2010 IEEE Wireless

Communications and Networking Conference (WCNC), Sydney, Australia, 2010, p. 6

6. J Qi, S Aissa, On the power amplifier nonlinearity in MIMO transmit beamforming

systems. IEEE Trans. Commun. 60(3), 876887 (2012)

7. PM Castro, JP Gonzalez-Coma, JA Garcia-Naya, L Castedo, Performance of MIMO

systems in measured indoor channels with transmitter noise. EURASIP J. Wirel. Commun.

Netw. no. 1, 19 (2012). doi:10.1186/1687-1499-2012-109

8. J Qi, S Aissa, Analysis and compensation of power amplifier nonlinearity in MIMO

transmit diversity systems. IEEE Trans. Veh. Technol. 59(6), 29212931 (2010)


17/30

15. TK Helaly, RM Dansereau, M El-Tanany, An efficient measure for nonlinear distortion

severity due to HPA in downlink DS-CDMA signals. EURASIP J. Wirel. Commun. Netw.

no. 1, 9 (2010). doi:10.1155/2010/945427. article ID 945427

16. IEEE Standard for Local and Metropolitan Area Networks- Parts 16: Air Interface for

Fixed and Mobile Broadband Wireless Access System, 2009

17. F Gregorio, J Cousseau, S Werner, T Riihonen, R Wichman, Power amplifier

linearization technique with IQ imbalance and crosstalk compensation for broadband MIMO-

OFDM transmitters. EURASIP J. Adv. Signal Process. no. 1, 15 (2011). doi:10.1186/1687-

6180-2011-19

18. SW Peters, RW Heath, The future of WiMAX: multihop relaying with IEEE 802.16j.

IEEE Commun. Mag. 47, 104111 (2009)

19. A Ghosh, R Ratasuk, B Mondal, N Mangalvedhe, T Thomas, LTE-advanced: next-

generation wireless broadband technology [Invited paper]. IEEE Trans. Wirel. Commun.

17(3), 1022 (2010)

20. AI Sulyman, G Takahara, H Hassanein, M Kousa, Multi-hop capacity of MIMO-

multiplexing relaying systems. IEEE Trans. Wirel. Commun. 8, 30953103 (2009)

21. FH Gregorio, Analysis and compensation of nonlinear power amplifier effects in multi-

antenna OFDM systems (Ph.D. dissertation, Helsinki University of Technology, Espoo,

Finland, 2007)

22. JJ Bussgang, Crosscorrelation functions of amplitude-distorted Gaussian signals, in

Research Lab. Electron, M.I.T, Technical Report, Cambridge, MA, USA, 1952, p. 216


18/30

29. S Woo, H Yu, J Lee, C Lee, J Laskar, Effects of RF impairments in transmitter for the

future beyond-3 G communications systems, in Proceedings of the 2006 IEEE International

Symposium on Circuits and Systems (ISCAS), Island of Kos, Greece, 2006, pp. 56685671

30. PB Kenington, RF and Baseband Techniques for Software Defined Radio, 1st edn.

(Norwood, MA, Artech House, 2005), p. 8

31. Y Rong, Y Xiang, Multiuser multi-hop MIMO relay systems with correlated fading

channels. IEEE Trans. Wirel. Commun. 10(9), 28352840 (2011)

32. Q Li, KH Li, KC Teh, Achieving optimal diversity-multiplexing tradeoff for full-duplexMIMO multihop relay networks. IEEE Trans. Inf. Theory 57(1), 303316 (2011)


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RH1H0H


20/30

(a)Nonlinear Multi Hop MIMO OFDM Communication Channel

S/P

CPremoval

DFT

amplification

InverseDFT

CPinsertion

P/S HPA

S/P

DFT

CPremova

l

amplification

InverseDFT

CPinsertion

P/S HPA

(b)Signal Processing at Relay Station (RS)

MIMO

OFDM

Encoder

HPA

HPA

MIMO

OFDM

Decoder

Relay

StationNx

1x

Nx

11y

Ny1

Ny1

1Dy

NDy

RH1H0H

1

1y1x

Figure 2

1AM-AM Conversion


21/30

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 20

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Ou

tputVoltage(N

ormalized)

Saleh Model

SEL Model

SSPA Model ( = .5)

SSPA Model ( = 5)

Figure 3 2.5


22/30

0 10 20 30 40 50 60 70 80 90 100

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Time

Signalamplitude

Figure 4

2.5CR 0dB


23/30

0 10 20 30 40 50 60 70 80 90 100

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

Time

Signalamplitude

CR = 0dB

CR = 6dB

Figure 5

-5


24/30

-10 -8 -6 -4 -2 0 2 4 6 8 10-50

-45

-40

-35

-30

-25

-20

-15

-10

frequency, MHz

powerspectraldensity[dB]

HPA Input Spectrum

HPA Output Spectrum (CR = 6dB)



-30.9 dB minimum, CR = 0dB

-36.1 dB minimum, CR = 4dB

-42.6 minimum, CR = 6dB

Figure 6

-5Transmit Spectrum at RS


25/30

-10 -8 -6 -4 -2 0 2 4 6 8 10-50

-45

-40

-35

-30

-25

-20

-15

-10

-5

powerspectralde

nsity[dB]

HPA Input Spectrum

HPA Output Spectrum at TS (Simulation, CR=1.4dB)

HPA Output Spectrum at TS (Analysis, CR = 1.4dB)

HPA Output Spectrum at RS (Simulation, CR=1.4dB)

HPA Output Spectrum at RS (Analysis, CR = 1.4dB)

-25.1 dB minimum, at RS

-33.0 dB minimum, at TS

Fi


26/30

-10 -8 -6 -4 -2 0 2 4 6 8 10-45

-40

-35

-30

-25

-20

-15

-10

-5

fequency, MHz


HPA Input Spectrum

HPA Output Spectrum at RS(1 hop)



-5


27/30

-10 -8 -6 -4 -2 0 2 4 6 8 10-50

-45

-40

-35

-30

-25

-20

-15

-10

frequency, MHz

powerspectrald

ensity[dB]

HPA Input Spectrum

HPA Output Spectrum, AF

HPA Output Spectrum, DemF

HPA Output Spectrum, DF

-22.7 dB minimum, AF

-25.3 dB minimum, DemF

-30.3 dB minimum, DF

Figure 9

0


28/30

-10 -8 -6 -4 -2 0 2 4 6 8 10-80

-70

-60

-50

-40

-30

-20

-10

frequency, MHz

powerspectra

ldensity[dB]

Filtererd, HPA Input Spectrum

Filtered, HPA Output Spectrum(CR=1.4dB)

Filtered, HPA Output Spectrum (CR=3dB)

Filtered, HPA Output Spectrum (CR=5dB)

Figure 10

0


29/30

-10 -8 -6 -4 -2 0 2 4 6 8 10-80

-70

-60

-50

-40

-30

-20

-10

frequency, MHz

powerspectra

ldensity[dB]


Filtered, HPA Output Spectrum at TS

Filtered, HPA Output Spectrum at RS, DemF(1 hop)

Filtered, HPA Output Spectrum at RS, DemF(2 hops)

Figure 11

0


30/30

-10 -8 -6 -4 -2 0 2 4 6 8 10-80

-70

-60

-50

-40

-30

-20

-10

frequency, MHz



Filtered, HPA Output Spectrum at TS

Filtered, HPA Output Spectrum at RS, DF, (1 hop)

Figure 12

spectral re-growth due to hpa nonlinearity

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